Diagnosis of thruster fault condition using statistical design of experiment

Diagnosis of thruster fault condition using statistical design of experiment

¹Mohd Akmal Mohd Yusoff, ²Mohd Rizal Arshad, & Muzammer Zakaria

Underwater Robotics Research Group (URRG), School of Electrical & Electronics Engineering, Engineering Campus, Universiti Sains Malaysia, 14300, Nibong Tebal, Seberang Perai Selatan, Penang, MALAYSIA

Email: ¹mamy.lm09@student.usm.my, ²rizal@eng.usm.my Received 26 July 2012; revised 18 August 2012

Present study consists the diagnosis of thruster fault condition using statistical design of experiment. Fault in thruster can cause deviation in process parameter, i.e. current load which could interfere with the propulsion system and overall system operation. The faulty conditions are demonstrated by blocked ducting. Variations of current load due to several conditions e.g. normal and faulty are studied using analysis of variance (ANOVA) and factorial design. Two-Factor factorial design is used to analyze the means in each factor. The two factors are the armature voltage and thruster condition. Tukey’s method is used to test all pair wise means in a single factor i.e. thruster condition in order to confirm the significant variation for each condition. Result from the experiment shows that the null hypothesis H0 for both Two-Factor factorial design and Tukey’s test are rejected and the alternate hypothesis H₁ is accepted. This indicates that the current loads for each pair are varying and all means in thruster condition factor are significantly different.

Keywords: Statistical Design of Experiment (DOE), Analysis of variance (ANOVA), Factorial design, Thruster fault diagnosis

Introduction

The increasing demand in Unmanned Underwater Vehicle (UUV) system applications has encouraged researchers to introduce new technique and method to improve the system safety and reliability. Many modern techniques in control system have been implemented in UUV. Author in¹ has presented on advances technologies in UUV including modeling, control and guidance. In general, there are two common types of UUV, the remotely operated vehicle (ROV) and autonomous underwater vehicle (AUV).

There are different modules and subsystems in UUV² e.g. control system, sensor and navigation, actuators, powers system and etc. Each module has a significant contribution towards UUV operability and performance. If one of the modules failed, it is possible that the whole UUV operation could be jeopardized. Hence, researcher has come out with a technique called Fault Tolerant Control (FTC) to compensate error due to failure in components³. The general framework of FTC consists of two main tasks; fault diagnosis and controller re-design^4-6 Fault diagnosis consists of several diagnostic steps, which are:

• Fault detection: Decide whether or not a fault has occurred. This step determines the time at which the system is subject to faults.

• Fault isolation: Find in which a components a fault has occurred. This step determines the location of the fault.

• Fault identification and estimation: Identify the fault and estimate its magnitude. This step determines the kind of fault and its severity.

All of the above terms can be concluded as Fault Detection and Diagnosis (FDD). In general, many works have been published on FDD methodologies and techniques since the introduction of fault tolerant control in the last three decades.

There are two types of FDD; model-based and model-free fault detection and diagnosis^7-8. Some of the model based FDD techniques are such parameter estimation, state observers, neural networks, state estimations, parity equations and principle components analysis. Meanwhile, model-free FDD are such limit checking and trend checking e.g.

fixed threshold, adaptive threshold and change detection methods . On the FDD of UUV’s actuator and thruster fault, many publications can be found focusing on difference aspects of fault diagnosis and identification^9-15.

In designing the fault tolerant control for ROV propulsion system i.e. thrusters, the thruster fault can be diagnosed by prediction or learning. Predictive method is an online method and usually based on

a robust or pre-determined model. On other hand, learning method requires an offline and real time situation where the thruster needs to be brought into faulty state so that its fault condition can be explicitly learned and used as a reference model in FTC.

However this method is limited to non destructive test otherwise the thruster could be damaged.

Therefore, predictive method and learning method can be implemented together to complement each other.

There are many established techniques of monitoring and diagnosing of electrical machines e.g. electrical motor such as time and frequency analysis, noise and vibration monitoring, harmonic analysis of motor torque and speed and etc¹⁶.

This paper presents an offline diagnosis of electric thruster fault by demonstrating the possible causes of the fault. The thruster condition can be characterized by process parameters i.e. motor armature voltage Vm and motor current load lm. The characterization of process parameter is emphasized on the current load variations due to two factors, armature voltage and thruster condition. In this work, the statistical design of experiment^17-18 i.e. analysis of variance (ANOVA) and Two-Factor factorial design is used to analyze the current load variations. Other technique to diagnose the motor fault is such as Motor Current Signature Analysis (MCSA)¹⁶. However, such method may require extra cost in order to acquire the appropriate testing apparatus e.g. diagnostic tools and software.

Materials and Methods

Characteristics of DC brushed Electric Thruster.

Electric thruster has been widely used in many UUV systems because it is easy to operate. Unlike engine driven thruster, electric thruster contributes to zero waste. However, the electric thruster is constantly exposed to wear and tear since it is a combination of electrical component i.e. motor and mechanical components i.e. rotary shaft and propeller.

Plus, electric thruster consumes the most electrical energy and produces constant heat. The heat, if not manage properly; can potentially cause failure to the thruster. As electric thruster is driven by an electric motor, it converts electrical energy to rotating kinetic energy to propel the rotary shaft. The rotating propeller produces thrust output in which result in the increase of the current load. The electro-mechanical relationship of electric thrusters can be modeled,

=0

−

−

+ _{a m m m m}

m

a I R I K V

dt

L d ω ^…(1)

=0 +

−K I Q

j_mⁿ _{m m} …(2)

where Vm is the motor armature voltage, lm motor armature current, La is the motor armature inductance, Ra is the motor armature resistance, jm is the rotor moment of inertia, Km is the motor torque constant, n is the propeller revolution and Q is the load from the propeller.

Since the electrical time constant

a a

a R

= L

τ

relatively small compared to the mechanical time constant, the time scale separation suggests that,

≈0

t im a a

d d R

L . Thus the Eq. 2 becomes,

=0

−

− _{m m m}

m

ai K V

R

ω

By combining Eq.3 and Eq.4, the motor voltage control can be represented as following equation,

Q R V

n K R

J K _m

a m a

n m

m+ ² = − ^…(4)

By modifying Eq.4, a unified representation of DC motor is given as,

Q n

K

J_mⁿ + _n =τ − ^…(5)

where

a m

n R

K K

= 2 is the linear damping coefficient

and _m

a mV R

= K

τ

From Eq. 2 and Eq. 3, it is shown that the motor current lm can be varied if the armature voltage or the propeller load is varied. For cases of fault, the external disturbances cause the propeller load, thus the motor current to vary. The variation of motor current need to be diagnosed and identified in order to make decision whether the deviation is harmful to the thruster itself and to the system in general, or not.

Fault detection and diagnosis of electric thruster A fault in a dynamical system is defined as a deviation of the system structure or the system parameters from the nominal situation⁴. Nominal system parameters is regarded as fault-free situation and usually made as the reference comparison towards the actual process parameter.

Let consider an electric thruster system with typical input-output model with disturbance that cause thruster failure. A basic principle of FDD is the consistency-based diagnosis as shown in Figure 1.

The consistency of the model can be checked at every time t by determining the difference of actual y(t) and reference (model) process parameters, ŷ(t),

e(t) = y(t) − ŷ (t) …(6)

The difference of reference and actual process parameters is called residual. In the faultless case, residual vanishes or is close to zero whereas non- vanishing residual indicates occurrence of fault.

The voltage-current relationship can be used for consistency checking of an operating thruster. The residuals can be specifically determined as the magnitude of armature voltage and current load residuals,

Armature voltage residual: e_v = v_act −v_ref ^…(7) Current load residual: e_i = i_act −i_ref ^…(8) The above step is called residual generation.

The residual needs to be evaluated in order isolate and identify the faults. In these steps, disturbance and measurement noise are taken into account to avoid false alarm. The evaluation of residuals is performed using design of experiment analysis.

In this work, the deviation of current load is the main interest since there is a very small deviation i.e. voltage drop between supplied voltage and the armature voltage.

Fig. 1—Diagnosis of electric thruster

Sampling of current load

Several sample of data sets of thrusters process parameter i.e. armature voltage and current load are measured and recorded from a controlled experiment. There are two conditions of thruster process parameters that need to be studied, normal process parameter and actual process parameter due to fault. There are several possible faulty conditions, but in this work three conditions are demonstrated:

1. Partially blocked ducting 2. Fully blocked ducting 3. Saturation

In real underwater environment, such condition like blocked ducting can be demonstrated as, e.g.

seaweed, underwater plant or marine life that get sucked into the water flow and accidently covering the ducting inlet or outlet. Unblock (normal), partially and fully blocked ducting is illustrated as in Figures 2, 3 and 4.

Fig. 2—Normal thruster condition

Fig. 3—Partially blocked ducting

To demonstrate the thruster fault, the water flow through the ducting is disturbed by blocking its pathway. Partially blocked ducting still allows a portion of thrust to go through the ducting outlet while full blocked might cause thrust to oscillate inside the ducting. Both scenarios cause the propeller loads i.e.

torque to increase and therefore current load fluctuates and deviates from its normal value. The current deviation is measured and analyzed for residuals.

To demonstrate thruster saturation, different technique is applied. A thruster is considered to be in saturation if the thruster reference input exceeds the particular output limit. In normal condition, the manufacturer datasheet provides that the minimum and maximum current loads allowed for operating the thruster is m4A. However, there are situations where saturation thruster saturation (ventilation) can occur.

Figure 5 shows a situation where the thruster propeller is at the borderline of water and air. This situation creates saturation or ventilation and usually happens when for example, an ROV is performing the heave motion; submerge and re-float routines, or the ROV is stranded at insufficient water depth. When this condition happens, the thruster allows both air and water to flow through the ducting. Since the thrust produced is not normal, the current load will deviates from its normal value, therefore is considered as an anomaly and will be taken into consideration in studying the thruster faulty condition.

Fig. 4—Fully blocked ducting

Fig. 5—Thruster saturation

Analysis of Variance (ANOVA)

In general, analysis of variance (ANOVA) can be described as a collection of statistical models and procedures to study and analyze the observed variance in a particular variable. The variance is partitioned or group into components that attribute to different sources of variation. There are several different tests and procedures that can be utilized in ANOVA.

In this work, ANOVA is presented as factorial design i.e. Two-Factor factorial design.

Tukey’s test

In many practical cases, the interest of study is to compare only pairs of means. Let consider that following an ANOVA, the null hypothesis of equal treatments is rejected. Then, all pair wise means comparisons need to be tested. For Tukey’s test, let consider the following hypothesis,

j

H₀:µi =µ …(9)

j

H₁:µi ≠µ …(10)

Tukey’s procedure makes use of the distribution of the studentized range statistic,

n MS

y q y

E/ max− min

= ^…(11)

where, ymax and ymin are the largest and smallest sample means, respectively from a group of p sample means. For equal sample sizes, Tukey’s test declares two means significantly different if the absolute value of their sample differences exceeds,

n f MS q

T_α = _α(

α

A set of 100(1 − α) percent confidence intervals for all pairs of means can be written as,

j i T y y T

y

y_i − _j − _α ≤µ_i −µ_j ≤ _i − _j + _α; ≠ ^…(13) Result and Discussion

1. Sampling of normal current loads

The scatter plots of normal/reference current load versus armature voltage for both forward and reverse thrust are shown as in Figures 6 and 7. Regression equation is constructed to show that the relationship between the armature voltage and current load is linear.

Fig. 6—Scatter plot of current load vs. armature voltage in forward thrust

Fig. 7—Scatter plot of current load vs. armature voltage in reverse thrust

The regression equation for Figure 6 is given as,

f ref f

ref V

I _. =−1.16+0.282 _. …(14)

The regression model for figure XX in given as,

r ref r

ref V

I _. =−1.11+0.273 _. ^…(15)

2. Two-Factor Factorial Design

This factorial design contains two factors, A and B.

Both factors have k level of factor A and l level of factor B. The general arrangement for a Two-Factor Factorial Design is described as in Table 1.

Table 1 – General arrangement of Two-Factor Factorial Design Factor B

1 l

Factor A 1

k

In this work, two factors of interest are the armature voltage and the thruster conditions with current load as the response. The armature voltage has 5 level of voltage (l=5) while the thruster has 4 levels of condition (k=4). Each set of data has five replications (n=5) measured and collected in randomized order generated by computer.

Factor A: Thruster condition = {N, PBD, FBD, S}

Factor B: Armature voltage = {12, 13, 14, 15, 16}

where,

N – normal condition

PBD – partially blocked ducting FBD – fully blocked ducting S – Saturation

To investigate whether each mean is equal or vary, let consider the following null and alternate hypotheses,

a

H₀:

µ

µ

µ

) , (

0: for atleastone pairof i j

H µ_i ≠µ_j …(17)

From ANOVA test, the P value determines whether to reject or accept the null hypothesis.

Table 2 shows the response, i.e. current load for each pair of factor, armature voltage and thruster condition. From the table, an ANOVA test is performed using Minitab 16 to test the hypothesis in Eq.16. The result is shown as in Table 3.

Table 2—Two-Factor Factorial Design Armature voltage Thruster

condition

12 13 14 15 16

N 2.234 2.544 2.804 3.092 3.352

PBD 2.482 2.762 2.962 3.324 3.64

FBD 2.702 3.006 3.302 3.64 3.974

S 0.69 0.784 0.864 0.916 0.998

Table 3—ANOVA, Current load vs. Factor A, Factor B

Source DF SS MS F P

Factor A 4 11.503 2.8758 1025.60 0.0000 Factor B 3 94.493 31.4977 11233.14 0.0000 Interaction 12 1.888 0.1573 56.11 0.0000

Error 80 0.224 0.0028

Total 99 108.109

DF is the degrees of freedom, SS is the sums of square, MS is the mean square and F is the ratio between mean square factor and error,

error factor

MS

F = MS …(18)

P is a value is the probability that quantifies the strength of the evidence against the null hypothesis H0, in favor of the alternate hypothesis, H1, From Table 3, all P values are computed close to zero. Therefore, the null hypothesis as in Eq. 9 is rejected for each factor. This proves that the current loads measured in this experiment are varying according to different armature voltage inputs and thruster conditions

Since the diagnosis of thruster fault is more emphasize on studying the response i.e. current load due to several conditions of thruster, thus it is the interest to study the response variation due to several thruster conditions. For this purpose, Tukey’s test is used to analyze the means of factor B. To run the Tukey’s tests, pair wise comparisons between levels in Factor A are computed as in Table 4.

From Eq.12, for level of confidence, α = 0.05, q0.05(0.05,80) ≅ 3.74 is obtained from Appendix Table VIII. pp.622¹⁶. Thus, for MSE = 0.0028 and n = 5, T0.05, can be computed as,

0885 . 5 0

0028 . 74 0 .

05 3

.

0 = =

T

By comparing T0.05 with means comparisons as in Table 4, it is showed that all means comparisons are larger than the computed T0.05. Therefore, the null hypothesis in Eq.11 is rejected. Therefore, it is proved that all means in thruster condition factor are significantly different. The current load can be characterized accordingly due to variation in thruster condition.

Table 4—Means Comparisons Armature voltage

Means differences 12 13 14 15 16

N-PBD 0.248 0.218 0.158 0.232 0.288 N-FBD 0.468 0.462 0.498 0.548 0.622

N-S 1.544 1.76 1.94 2.176 2.354

PBD-FBD 0.22 0.244 0.34 0.316 0.334 PBD-S 1.792 1.978 2.098 2.408 2.642 FBD-S 2.012 2.222 2.438 2.724 2.976

Conclusion

As conclusion, statistical design of experiment is a powerful tool to analyze thruster process parameter, i.e. current load that is subject to fault. From computation, it is shown that means of current load is significantly different according to thruster condition that are under study. Thus the severity of thruster due to fault can be estimated and classified.

Acknowledgement

The authors would like to thanks people in Underwater Robotics Research Group (URRG), Universiti Sains Malaysia for their sincere advice and consultation support. Special appreciation to the Ministry of Higher Education and Ministry of Science Technology and Innovation for their continuous support for the unmanned underwater vehicle projects at URRG Laboratory. This research work is supported by Prototype Research Grant Scheme (PRGS - 6740003) under Ministry of Higher Education.

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